In the deterministic setting, there exists a plethora of literature that settles tractability and stability of model-based predictive control, see, for example, [1]}, [2]}, [3]}, [4]} and the references therein. However, there are fewer results in the stochastic case, some of which we outline next. In [5]}, the authors reformulate the stochastic programming problem as a deterministic one with bounded noise and solve a robust optimization problem over a finite horizon, followed by estimating the performance when the noise can take unbounded values, i.e., when the noise is unbounded, but takes high values with low probability (as in the Gaussian case). In [6]}, [7]} a slightly different problem is addressed in which the noise enters in a multiplicative manner into the system, and hard constraints on the state and control input are relaxed to probabilistic ones. Similar relaxations of hard constraints to soft probabilistic ones have also appeared in [8]} for both multiplicative and additive noise inputs, as well as in [9]}. There are also other approaches, for example those employing randomized algorithms as in [10]}, [11]}. Finally, a related line of research can be found in [12]}, and a novel convex analysis dealing with chance and integrated chance constraints can be found in [13]}.
